The European vulnerable option pricing based on jump-diffusion process in fractional market

Assuming that the underlying asset is driven by a fractional Brownian motion with jumps, the interest rate and the default intensity are both following the Vasicek model, we derive the European vulnerable option pricing in fractional market. Then the martingale method and measure transformation are used to deduce the solution of it. On the other hand, the expression of jump process in the form of measure transformation is proved in this paper which can be regarded as a supplement of the Girsanov's theorem. The results are tested through numerical experiments which show that the pricing model proposed in this paper can describe the changes of the financial asset well, it makes the pricing more accords with the realistic than Black-Scholes option pricing model.